MathDB

A representation of

\frac{17}{20}

as a sum of reciprocals

\frac{17}{20} = \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_k}

is called a calm representation with

k

terms if the

a_i

are distinct positive integers and at most one of them is not a power of two.
(a) Find the smallest value of

k

for which

\frac{17}{20}

has a calm representation with

k

terms. (b) Prove that there are infinitely many calm representations of

\frac{17}{20}

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